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A planet is in a circular orbit of large radius around the Sun with orbital speed $\frac{u}{0.207}$ . The planet has no rotation about its own axis and the escape speed from the planet is $u$ . The minimum relative velocity that has to be imparted to a body on the surface of the planet is $k u$ to escape from the solar system. Find the value of $k$ .

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answer is 2.22.

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Detailed Solution

$V = \sqrt{V_{e}^{2} + {(\sqrt{2} - 1)}^{2} V_{0}^{2}} = 2.236 u$

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